Various types of nuclear fuel cladding of initial cladding thickness $540$ microns have been exposed to high temperature water in reactor environments and the amount of corrosion in each case $($corrosion layer thickness$)$ is plotted below.

It is known that the Pilling Bedworth ratio for zirconium oxide formation is $1\mathrm{.}56,$ the $Zr$ atomic mass is $91$ and that of oxygen is $16.$ The density of $Zr$ is $6\mathrm{.}5\frac{g}{c}{m}^3$ and that of $Zr{O}_2$ oxide is $5\mathrm{.}68\frac{g}{c}{m}^3.$

For the point in the red and blue circles, what would be the hydrogen content in wt$.$ ppm if:

a$)$ the hydrogen pickup fraction was $15\%(10)$

b$)$ if the hydrogen pickup fraction was $100\%?(5)$

c$)$ the points in the plot span a wide variety of corrosion thicknesses. What in your view are some of the possible reasons for the differences in corrosion rates?$(5)$